\section{Pre-Processing}
For making the algorithm a little faster some data can be remove "obvious" structure. A good example to remove user and item means where missing entries is ignored

$R_{mu} \leftarrow R_{mu} - \frac{1}{U_{m}} \sum_{s} R_{ms} - \frac{1}{M_{u}} \sum_{r} R_{ru} + \frac{1}{N} \sum_{s} \sum_{r} R_{sr}$

where:
\begin{itemize}
\item $R$ is the collection of data.
\item $U_{m}$ is the total number of observed rating for items $m$.
\item $M_{u}$ is the total number of observed rating for users $u$.
\item $N$ total number of observed item-user pairs.
\end{itemize}